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    Calculating long run equilibrium price and output level

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    Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by following linear demand function:

    P= 200-QA-QB

    Where QA and QB are quantities sold by the respective firms and P is the selling price. Total costs functions for the two companies are

    TCA = 1,500 + 55QA +Q2A
    TCB= 1,200+20QB +2Q2B

    Assume that the firms act independently as in cournot model (i.e., each firm assumes that the other firm's output will not change)

    a. Determine the long-run equilibrium output and selling price for each firm
    b. Determine firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).

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    https://brainmass.com/economics/general-equilibrium/calculating-long-run-equilibrium-price-and-output-level-402193

    Solution Preview

    a. Determine the long-run equilibrium output and selling price for each firm.

    In cournot competition firms compete in quantities and tend to maximize their profit
    P=200-QA-QB

    In case of company A
    Total Revenue =TRA=P*QA=(200-QA-QB)*QA=200QA-QA^2-QAQB
    Marginal Revenue=MRA=d(TRA)/dQA=200-2QA-QB

    TCA=1500+55QA+QA^2
    Marginal ...

    Solution Summary

    This solution describes the steps to calculate long run equilibrium output and selling price for each of the given firms. It also calculates total industry profits.

    $2.19